Question

# The length of the common chord of two intersecting circles is 30 cm. If the diameters of these two circles are 50 cm & 34 cm, the distance between their centers is ____ cm.

A

30

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B
28
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C
24
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D
32
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Solution

## The correct option is D 28 The perpendicular drawn from centre of the circle bisects the chord. OO' bisects the chord AB into two equal parts of 15 cm each. AC = CB = 15cm Now applying Pythagoras theorem to ΔOAC, we get (25)2 = (15)2 + (x)2 625 = 225 + (x)2 ⟹ x = 20 cm Now, applying Pythagoras theorem in ΔO'AC we get, (17)2 = (15)2 + (y)2 289 = 225 + (y)2 y = 8 cm Therefore distance between the two centres is (x+y)=(20+8)=28 cm.

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